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This task examines the ways in which the plane can be covered by regular polygons in a very strict arrangement called a regular tessellation. These tessellations are studied here using algebra, which enters the picture via the formula for the measure of the interior angles of a regular polygon (which should therefore be introduced or reviewed before beginning the task). The goal of the task is to use algebra in order to understand which tessellations of the plane with regular polygons are possible.

الموضوع:
الرياضيات
علم الجبر
هندسة الشكل
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
01/21/2013 Unrestricted Use
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في هذه المهمة يكون على الطلاب تفسير تعبيرات تنطوي على اثنين من المتغيرات في سياق وضع العالم الحقيقي. يمكن تفسير جميع أشكال التعبير على أنها الكميات التي يمكن للمرء أن يدرسها عند البحث في اثنين من قطعان الحيوانات.

الموضوع:
الرياضيات
علم الجبر
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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In this problem students are comparing a very small quantity with a very large quantity using the metric system. The metric system is especially convenient when comparing measurements using scientific notations since different units within the system are related by powers of ten.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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This task requires students to work with very large and small values expressed both in scientific notation and in decimal notation (standard form). In addition, students need to convert units of mass.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
08/21/2012 Unrestricted Use
CC BY
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مهمة خلط الطلاء هذه تتطلب من الطلاب تسجيل النسب في نظام الإحداثيات. انها لغة قياسية في مسائل النسب.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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مهمة خلط الطلاء هذه تتطلب من الطلاب تسجيل النسب في نظام الإحداثيات. انها لغة قياسية في مسائل النسب.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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في هذا العالم الحقيقي المليء بالمشاكل يحل الطلاب المسائل على أساس العلاقة بين تكاليف الإنتاج والأسعار.

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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
05/01/2012 Unrestricted Use
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توفر هذه المهمة سياق العالم الحقيقي لتفسير وحل المعادلات الأسية. هناك نوعان من الحلول المقدمة للجزء (أ). يوضح الحل الأول كيفية استخلاص الاستنتاج من خلال التفكير من حيث الوظائف ومعدلات تغيرها. يوضح النهج الثاني عرض جبري صارم بأن المجموعتين السكانيتين لا يمكن أبدا أن تكون متساوية.

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Activity/Lab
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Illustrative Mathematics
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Illustrative Mathematics
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Illustrative Mathematics
05/01/2012 Unrestricted Use
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هذه مهمة حقيقية تتطلب من الطلاب الإجابة عن أسئلة حول معادلاتٍ لحساب الفائدة المركبة.

الموضوع:
الرياضيات
علم الجبر
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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هذه المهمة تتطلب من الطلاب استخدام التشابه لحل المشكلة في السياق الذي سيكون مألوفا للكثيرين، على الرغم من أن معظم الطلاب اعتادوا على استخدام الحدس بدلا من التفكير الهندسي لاعداد اللقطة التصويرية.

الموضوع:
الرياضيات
هندسة الشكل
علم المثلثات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
08/21/2012 Unrestricted Use
CC BY
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This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.

الموضوع:
الرياضيات
علم الجبر
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
10/21/2013 Unrestricted Use
CC BY
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This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

الموضوع:
الرياضيات
علم الجبر
وظائف
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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من الملائم في هذه مهمة استخدام الطلبة للتكنولوجيا كالآلة الحاسبة البيانية أو حزمة من البرامج الرياضية المجانية، مما يجعل منها أدوات مفيدةً للطلاب للانخراط في معيار رقم 5 في تعليم الرياضيات باستخدام الأدوات المناسبة استراتيجيًا.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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This task requires students to solves multistep ratio and percent problem.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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This problem involves the meaning of numbers found on labels. When the level of accuracy is not given we need to make assumptions based on how the information is reported. The goal of the task is to stimulate a conversation about rounding and about how to record numbers with an appropriate level of accuracy, tying in directly to the standard N-Q.3. It is therefore better suited for instruction than for assessment purposes.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
01/05/2013 Unrestricted Use
CC BY
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This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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This problem includes a percent increase in one part with a percent decrease in the remaining and asks students to find the overall percent change. The problem may be solved using proportions or by reasoning through the computations or writing a set of equations.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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This task presents a real world situation that can be modeled with a linear function best suited for an instructional context.

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الرياضيات
وظائف
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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In this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information provided by tables, graphs and equations.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
08/08/2012 Unrestricted Use
CC BY
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Students are exptected to identify the slope of the line with the unit rate in this real world problem.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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The primary purpose of this problem is to rewrite simple rational expressions in different forms to exhibit different aspects of the expression, in the context of a relevant real-world context (the fuel efficiency of of a car). Indeed, the given form of the combined fuel economy computation is useful for direct calculation, but if asked for an approximation, is not particularly helpful.

الموضوع:
الرياضيات
علم الجبر
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
01/25/2013 Unrestricted Use
CC BY
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This task gives students an opportunity to work with exponential functions in a real world context involving continuously compounded interest. They will study how the base of the exponential function impacts its growth rate and use logarithms to solve exponential equations.

الموضوع:
الرياضيات
وظائف
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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Students must calculate the volume of a cone in this real world task.

الموضوع:
الرياضيات
هندسة الشكل
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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The purpose of the task is for students to compare signed numbers in a real-world context.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
07/23/2012 Unrestricted Use
CC BY
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Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

الموضوع:
الرياضيات
هندسة الشكل
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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This task asks the students to solve a real-world problem involving unit rates (data per unit time) using units that many teens and pre-teens have heard of but may not know the definition for. While the computations involved are not particularly complex, the units will be abstract for many students.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
12/14/2012 Unrestricted Use
CC BY
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This task gives students the opportunity to verify that a dilation takes a line that does not pass through the center to a line parallel to the original line, and to verify that a dilation of a line segment (whether it passes through the center or not) is longer or shorter by the scale factor.

الموضوع:
الرياضيات
هندسة الشكل
علم المثلثات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.

الموضوع:
الرياضيات
علم الجبر
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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In this task students have the opportunity to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

الموضوع:
الرياضيات
وظائف
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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This real world problem is appropriate for mental mathematics and students should be encouraged to think through the solution mentally.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade.

الموضوع:
الرياضيات
هندسة الشكل
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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In this task students are asked to write an equation to solve a real-world problem. There are two natural approaches to this task. In the first approach, students have to notice that even though there is one variable, namely the number of firefighters, it is used in two different places. In the other approach, students can find the total cost per firefighter and then write the equation.

الموضوع:
الرياضيات
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing.

الموضوع:
الرياضيات
هندسة الشكل
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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The example of rabbits and foxes was introduced in the task (8-F Foxes and Rabbits) to illustrate two functions of time given in a table. We are now in a position to actually model the data given previously with trigonometric functions and investigate the behavior of this predator-prey situation.

الموضوع:
الرياضيات
وظائف
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
08/29/2012 Unrestricted Use
CC BY
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The example of rabbits and foxes was introduced in 8-F Foxes and Rabbits to illustrate two functions of time given in a table. The same situation was used in F-TF Foxes and Rabbits 2 to find trigonometric functions modeling the data in the table. The previous situation was somewhat unrealistic since we were able to find functions that fit the data perfectly. In this task, on the other hand, we do some legitimate modelling, in that we come up with functions that approximate the data well, but do not perfectly match, the given data.

الموضوع:
الرياضيات
وظائف
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
08/30/2012 Unrestricted Use
CC BY
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This task can be played as a game where students have to guess the rule and the instructor gives more and more input output pairs. Giving only three input output pairs might not be enough to clarify the rule.

الموضوع:
الرياضيات
وظائف
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
10/30/2013 Unrestricted Use
CC BY
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This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a Ňdouble-naped coneÓ with vertex at the center of the sphere and bases equal to the bases of the cylinder.

الموضوع:
الرياضيات
هندسة الشكل
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
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This exploration can be done in class near the beginning of a unit on graphing parabolas. Students need to be familiar with intercepts, and need to know what the vertex is.

الموضوع:
الرياضيات
علم الجبر
وظائف
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
05/01/2012 Unrestricted Use
CC BY
Rating
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This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.

الموضوع:
الرياضيات
علم الجبر
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics
08/07/2012 Unrestricted Use
CC BY
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While not a full-blown modeling problem, this task does address some aspects of modeling as described in Standard for Mathematical Practice 4. Also, students often think that time must always be the independent variable, and so may need some help understanding that one chooses the independent and dependent variable based on the way one wants to view a situation.

الموضوع:
الرياضيات
وظائف
نوع المادة:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
المؤلف:
Illustrative Mathematics